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What are equivalent swimming and running speeds?@Rider_X I don't remember exactly but I suspect that I did OLS regression. As for heteroscedasticity, recall that OLS produces unbiased though inefficient estimates so the coefficients will be right on average but statistical inference may be off. In any event, I was just doing this to show how one might approach the problem -- you might want to also look at this related answer.

What are equivalent swimming and running speeds?@PeterDeWeese Agreed, and even doing this for a sprint triathlon might give different results than for an Ironman. Note also that if we looked at the run-swim times rather than the quantiles, the correlation is .588, which indicates that swim time explains about 35% of the variance in run time. But this analysis still gives a way to think about how to answer a question like this.

Oct11

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What are equivalent swimming and running speeds?1) Well, if you were interested in, say 10k pace, you could convert from min/10k to min/mile, then use the regression line to get the swim pace, then convert that to, say, pace per 100 meters. 2) This is for multisport athletes and covers a wider range of abilities, so you might think of it as the "equivalent running and swimming pace for someone who does both sports." Ryan was looking at comparing record times for single-sport athletes. And 3) you'll find a slightly different relationship if you had used 2010 data, or a shorter race. I was just showing how one might address the problem.

Power while swimming?The relationship between heart rate and either speed or power in cycling, running, and rowing is quite variable so heart rate in those disciplines tends not to be a particularly good predictor of power output. For example, in cycling the correlation between heart rate and power is often around r = +0.5. More to the point, if we know what the relationship between speed and power is, we can estimate what the drag is -- which can help us figure out how to reduce that drag and improve speed.

Power while swimming?It's what's called a scatterplot matrix. They display a bunch of regular two-way scatterplots. Look at the top row: the y-axis for the entire top row is overall time and the x-axis for each of the plots is the swim time, the bike time, and the run time. You can see the scale for the axes in the margins. The extreme right hand column are scatterplots where the x-axis is run time. Taken all together, you can see how the elapsed time for one leg is related to the elapsed time for the other two disciplines, and the overall time.